Related papers: Progress in lattice algorithms
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small…
A grand canonical system of non-interacting fermions on a square lattice is considered at zero temperature. Three different phases exist: an empty lattice, a completely filled lattice and a liquid phase which interpolates between the other…
Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques,…
We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a string-like structure with the newly created particles…
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…
We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work (Phys. Rev. E 76, 036704 (2007)) which provides a clear understanding in terms of…
Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a…
We derive a lattice approximation for a class of equilibrium quantum statistics describing the behaviour of any combination and number of bosonic and fermionic particles with any sufficiently binding potential. We then develop an intuitive…
In this contribution we give an introduction to the foundations and methods of lattice gauge theory. Starting with a brief discussion of the quantum mechanical path integral, we develop the main ingredients of lattice field theory:…
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called…
We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to…
We introduce a dynamical fermion algorithm which is based on the hybrid Monte Carlo (HMC) algorithm, but without pseudofermions. The molecular dynamics steps in HMC are retained except the derivatives with respect to the gauge fields are…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
In this work we investigate theoretical and computational aspects of novel lattice fermion formulations for the simulation of lattice gauge theories. The lattice approach to quantum gauge theories is an important tool for studying quantum…
The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo…
Learned field transformations may help address ubiquitous critical slowing down and signal-to-noise problems in lattice field theory. In the context of an annealed sequence of distributions, field transformations are defined by integrating…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems.…
The worldsheet formulation of lattice gauge theories has two appealing features: the gauge non-redundancy and the geometrical transparency. Both properties are profitable in order to perform numerical computations. In the case of dynamical…